Behavior of Magnetization and NMR Signals

Some examples may help to clarify the steps involved in 2D NMR. Consider first the pulse sequence shown in Fig. 10.2 applied to a molecule with a single NMR frequency (e.g., the H resonance of CHCl3).The preparation period is simply a 

For a given value of q, we can Fourier transform the FID with respect to the variable t2 to obtain a spectrum 

After the system has relaxed back to equilibrium, the process is repeated, but now M is allowed to precess for a longer value of q, and the signal is detected and Fourier transformed. The absorptive portion of a set of spectra obtained for a set of different f, values is sketched in Fig. 10.3a. The amplitude of the resonance at F2 = ft2/2 jr is modulated by cos ft,q, as shown more clearly in Fig. 10.3b, where the data matrix has been transposed in the computer. The value of this modulation frequency can be obtained from a second Fourier transformation, this time with respect to q. If 2N data points are acquired for each value of q, the 

FIGURE 10.3 Data from the 2D pulse sequence in Fig. 10.2. (a) Spectra resulting from Fourier transform of S(t2) at various values of f,. (f ) Rotation of axes in (a) to show modulation in signal amplitude as a function of. (c) Signal after second Fourier transform with respect to showing a single peak at coordinates (Q,t/2TT, D./27T). (d) Contour plot, showing the peak from (c). Courtesy of Ad Bax (National Institutes of Health). 

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